Liverpool have submitted a third offer for Philippe Coutinho and are adamant it is their final attempt to persuade Internazionale to sell the talented Brazilian midfielder.

They have again offered around £8m for the 20-year-old, a fee that Inter rejected on Wednesday, but their latest bid increases the amount the Italian club would receive up front. Liverpool's previous offers were heavily incentivised and therefore did not appeal to a club that is seeking to reduce its debt in this transfer window.

Inter have accepted £10.2m from Southampton for Coutinho, who played under their new manager, Mauricio Pochettino, while on loan at Espanyol last season, but the player has told his employers he is not interested in a move to St Mary's Stadium. That has encouraged Liverpool's belief that a deal can be struck for less, although £8m also reflects the value their scouting network have placed on the midfielder. Liverpool are pressing for an answer from Inter this weekend as they would need to apply for a work permit for Coutinho, whose one senior appearance for Brazil does not meet the criteria.

Brendan Rodgers, meanwhile, has challenged Liverpool to leave him out of pocket by reproducing the form that beat Norwich City 5-0 last weekend against Oldham in the FA Cup on Sunday and Arsenal in the Premier League next midweek.

The Liverpool manager vowed to take the entire first-team squad for a meal before Christmas providing they won three consecutive games, a sequence they recorded against Queens Park Rangers, Sunderland and Mansfield Town. He fulfilled the promise last Friday before the Norwich rout and will repeat the exercise once Liverpool produce another hat-trick of wins.

Rodgers said: "I took the players to San Carlo because I told them that, going into the new year, I would pay for lunch if we got three wins on the trot. Maybe I should have tried it in August. When they won at Mansfield one of the first things they said in the changing room afterwards was: 'You better get your money out.'

"Team spirit is important and, even though it was just a nice lunch, the more you are together and you can do that your spirit grows. The players enjoyed it so we have started the run again and it is me to pay again. I realised it could cost me when Glen Johnson was having apple tart. I might have to limit it to a main meal but I don't mind, I will do anything to get us winning. We will stick at getting three wins for now and then, once I am out of money, we can increase the target."